I find people that want demos are just looking for a free version of the game
That's a nice sweeping statement to make.
Besides, how would/could a demo constitute a free game?
Nothing of the sort and a ridiculous statement, made all the worse by your "demo of a boardgame" analogy.
Demos can be very productive in sales, but they can also be very counter productive.
As pointed out, some games lend themselves to a demo, some lend themselves to flash demostrations, others just cannot do with a demo because they are too complex. Taking all that into account with the financial side of things. A demo isn't just a cut down game, it's a re-write of the manual to give enough information to the user to allow them to make an educated determination of the game.
FPS games lend themselves very easily to demos. There is very little difficulty in FPS games. Some flight sims also lend themselves very easily to playable demos...others (like the upcoming Black Shark) do not. I would guess strategy games lend themselves less to playable demos...but that doesn't rule out demos across the board.
Some are simple enough to warrant a demo because it would take very little time to create a demo. However, these ones are probably most likely priced budget and as such maybe fall into the financial side of not allowing a demo.
I always point out my own personal experience...I tried the demo of airborne Assault:Red Devils Over Arnhem and I just didn't get it. So I dropped it like a hot brick. It wasn't until I saw it at budget and gave it another go and realised it was one of the best gaming systems (and AI) I had come across in a strategy game. In this instance, for me, the demo lost a sale initially. That's partly to do with the fact that the demo wasn't as intuitive as it could've been (I don't remember much documantation with it, but my memory is fading fast these days).
So it isn't a cut and dry "There should be a demo" or "There will not be a demo"...it depends on a lot of factors.
Generally, though, there is a plethora of information on the web about games. Sure, it doesn't mean you will like it, but the information is generally such that you can make up your mind by reading up on it...so there is really no need to waste money by buying a game you don't like (then blaming it on there being no demo) and no reason to avoid games because there is no demo...read up. Ask questions. You'll be able to make your own mind up.